Neutrinos Faster than the Speed of Light.

Noodle, I guess what meatloaf is getting at is that FTL (at least very slightly FTL) does not necessarily lead to a violation of causality. All examples and mathematical thought experiments of causality breaking during FTL use singularly extreme boundary conditions. The problem with these "proofs" is that causality breaking can only be wrapped in a mathematical sense under these obviously extreme examples. It is not possible to phrase causality as a general mathematical condition onto the Lorentzian transformation, it is hence not possible (at least to my feeble mathematical attempts) to rigorously prove that there are transformation solutions where causality can be conserved. Additionally, by fiat of the very definition of the Lorentzian, it is impossible to say anything about FTL.

Exactly. Basically, we can't draw any solid conclusions about FTL travel violating causaility, because have no math that has been tested to be relevant in FTL situations - Lorentz transformations all go to infinity when you put in C, or else to zero. They're asymptotic when they approach C, and we have not been able to prove that the are symmetrically applicable to particles travelling at FTL speeds - so we have no way of knowing that the projections we throw out using those equations are in fact relevant.

If the math shows a huge divergence when you approach a limit, it's quite likely that- IF - there exists FTL travel, it will require new math that is both applicable to FTL AND which reduces to explain all phenomena that goes at LTL speeds - sort of like how general relativity encompasses classical motion - only on a higher level.

Okay, so how hard would it be to set up a causality violation with this communication system? The emitter and detector are in different reference frames, so there should be some difference in timing. If we were able to get attosecond resolution on neutrino detectors, would we be able to set up a grandfather paradox?

Okay, so how hard would it be to set up a causality violation with this communication system? The emitter and detector are in different reference frames, so there should be some difference in timing. If we were able to get attosecond resolution on neutrino detectors, would we be able to set up a grandfather paradox?

Your reference frame would need to go this >< close up to light speed (for all intents and purposes actually indistinguishable from light speed) to cause the necessary distortion of space-time and shortening of distances to get into any kind of grandfathering paradox.

But here, I do have to pose an interesting though experiment:Can Neutrinos interact at all with such fast reference frames? The only reference frame known to be this fast are photons, and photons cannot interact with neutrinos directly! As far as I am aware (HatMonster please correct me), only mass bearing Hadrones or Leptons can interact with neutrinos. But it is practically impossible to accelerate this kind of matter to light speed. Doing so would convert it into mass-less photons!

So, can there be a paradox if these special neutrinos cannot interact with those reference frames, that would cause a paradox?

Exactly. Basically, we can't draw any solid conclusions about FTL travel violating causaility, because have no math that has been tested to be relevant in FTL situations - Lorentz transformations all go to infinity when you put in C, or else to zero. They're asymptotic when they approach C, and we have not been able to prove that the are symmetrically applicable to particles travelling at FTL speeds - so we have no way of knowing that the projections we throw out using those equations are in fact relevant.

If the math shows a huge divergence when you approach a limit, it's quite likely that- IF - there exists FTL travel, it will require new math that is both applicable to FTL AND which reduces to explain all phenomena that goes at LTL speeds - sort of like how general relativity encompasses classical motion - only on a higher level.

You and troy said you had trouble visualizing causality and relativity of simultaneity. I was responding to your hypothetical FTL bullet scenario. If any observer sees the target struck before the gun is fired, causality is out the window. If you instead say that what that observer saw isn't really what happened, equivalence is out the window. This doesn't come from the math; this is by definition of those terms.

If we're speculating, and by all means let's, we should first be clear what we're speculating about. Assume there is FTL travel that requires a new theory and new math which reduces to our current understanding. That theory and that math would have to forbid your hypothetical just as much as Relativity does. If any observer could see an effect precede its cause, either causality or equivalent frames have to go. Supposing FTL does exist, some observer would have to measure it as faster than light while at the same time all observers must report the gun fires before the target is struck. That is what the new transform/math/theory would have to account for.

You and troy said you had trouble visualizing causality and relativity of simultaneity. I was responding to your hypothetical FTL bullet scenario. If any observer sees the target struck before the gun is fired, causality is out the window. If you instead say that what that observer saw isn't really what happened, equivalence is out the window. This doesn't come from the math; this is by definition of those terms.

If we're speculating, and by all means let's, we should first be clear what we're speculating about. Assume there is FTL travel that requires a new theory and new math which reduces to our current understanding. That theory and that math would have to forbid your hypothetical just as much as Relativity does. If any observer could see an effect precede its cause, either causality or equivalent frames have to go. Supposing FTL does exist, some observer would have to measure it as faster than light while at the same time all observers must report the gun fires before the target is struck. That is what the new transform/math/theory would have to account for.

I'm going to display my ignorance and join the 'trouble visualizing causality and relativity of simultaneity' camp. Why do all observers have to report the gun fires before the target is struck? Someone moving past the target at FTL speed could see the target struck, then move past the photon wavefront of the event to a point where the light bouncing off the trigger just as it's getting pulled is arrving. I don't see how this is moving back in time, but merely trading distance for observability. If he tries to FTL travel back to the target to warn him to duck, he'll see events happen as he gets closer to the target and arrive at a bleeding dead body. The activities of the gunfight would appear to speed up as he got closer as he raced back along the photonic wavefronts of events. At no time, though, would he be violating causality anymore than seeing someone die in front of you to a 2 mile distant sniper violates causality just because the sound of the gunshot hasn't gotten to you yet. It's an observational error due to positional change.

Hat Monster wrote:

I have planet A, planet B and planet C. They are arranged thus:

Code:A B C+--------------------------+

B is equidistant from both A and C. A and C have a wormhole connecting their low orbital domain, shown beneath them in the rendering above.

B does not like A or C and launches planet-killer missiles at both planets such as they arrive at the same time in B's frame of reference.

A scout from C is in orbit of A and sees A explode. C has not yet exploded from A's reference frame, so the scout quickly warns C through the wormhole, who are then able to activate defences and intercept the missile.

C is not destroyed, but A is. We have, however, violated causality. The extension below will show you how.

Now then, place scouts at BOTH planet A and C. Both scouts see the planet they are at destroyed and both go to warn the other, which to them is not destroyed and has ample time to erect defences once the scout zips through the wormhole.

The scout from C in orbit about A sees A explode. He looks up in the sky and sees C still floating there, as the light arriving is from some time back. Over his ear-mounted Wormhole Radio, though, all he hears is 'AAAAAAAAAAAARRRRGGGGH!!!!!! *boom*'

Intellectually I'm sure these responses are wrong (I don't yet have enough hubris to fault Einstein), but from a visualization exercise I can't intuitively grasp why.

You and troy said you had trouble visualizing causality and relativity of simultaneity. I was responding to your hypothetical FTL bullet scenario. If any observer sees the target struck before the gun is fired, causality is out the window. If you instead say that what that observer saw isn't really what happened, equivalence is out the window. This doesn't come from the math; this is by definition of those terms.

If we're speculating, and by all means let's, we should first be clear what we're speculating about. Assume there is FTL travel that requires a new theory and new math which reduces to our current understanding. That theory and that math would have to forbid your hypothetical just as much as Relativity does. If any observer could see an effect precede its cause, either causality or equivalent frames have to go. Supposing FTL does exist, some observer would have to measure it as faster than light while at the same time all observers must report the gun fires before the target is struck. That is what the new transform/math/theory would have to account for.

I'm going to display my ignorance and join the 'trouble visualizing causality and relativity of simultaneity' camp. Why do all observers have to report the gun fires before the target is struck? Someone moving past the target at FTL speed could see the target struck, then move past the photon wavefront of the event to a point where the light bouncing off the trigger just as it's getting pulled is arrving. I don't see how this is moving back in time, but merely trading distance for observability. If he tries to FTL travel back to the target to warn him to duck, he'll see events happen as he gets closer to the target and arrive at a bleeding dead body. The activities of the gunfight would appear to speed up as he got closer as he raced back along the photonic wavefronts of events. At no time, though, would he be violating causality anymore than seeing someone die in front of you to a 2 mile distant sniper violates causality just because the sound of the gunshot hasn't gotten to you yet. It's an observational error due to positional change.

Hat Monster wrote:

I have planet A, planet B and planet C. They are arranged thus:

Code:A B C+--------------------------+

B is equidistant from both A and C. A and C have a wormhole connecting their low orbital domain, shown beneath them in the rendering above.

B does not like A or C and launches planet-killer missiles at both planets such as they arrive at the same time in B's frame of reference.

A scout from C is in orbit of A and sees A explode. C has not yet exploded from A's reference frame, so the scout quickly warns C through the wormhole, who are then able to activate defences and intercept the missile.

C is not destroyed, but A is. We have, however, violated causality. The extension below will show you how.

Now then, place scouts at BOTH planet A and C. Both scouts see the planet they are at destroyed and both go to warn the other, which to them is not destroyed and has ample time to erect defences once the scout zips through the wormhole.

The scout from C in orbit about A sees A explode. He looks up in the sky and sees C still floating there, as the light arriving is from some time back. Over his ear-mounted Wormhole Radio, though, all he hears is 'AAAAAAAAAAAARRRRGGGGH!!!!!! *boom*'

Intellectually I'm sure these responses are wrong (I don't yet have enough hubris to fault Einstein), but from a visualization exercise I can't intuitively grasp why.

Here's another example.

Cartman and Kyle are going to try an experiment. Kyle will board a ship that can travel at 99.999% the speed of light, and begin heading towards Alpha Centauri. When Kyle gets Cartman's message, he will respond with what time his clock says.

Kyle gets on the ship and begins traveling. Ten minutes later, Cartman sends out a signal with a powerful laser. Kyle gets the signal around 1.9 years later (in Cartman's reference frame).

To Kyle, just about 3 days have elapsed, and so he quickly sends a signal back to Cartman.

Cartman receives this signal 3.8 years after he sent the original signal.

----

Now, we'll use Cartman's instantaneous communication technique.

10 minutes after Kyle leaves, Cartman uses the communicator. Kyle gets the message about 2 seconds after Cartman sent it (in Kyle's reference frame). Kyle bounces the message back to Cartman.

But but but.... what reference frame should we use? Kyle says that Cartman left him 2 seconds ago! So, according to Kyle, Cartman should get the message at time 2 seconds -- and that's before Cartman sent the message. So, there's now no reason for Cartman to send his message, since Kyle already got it.

I'm going to display my ignorance and join the 'trouble visualizing causality and relativity of simultaneity' camp. Why do all observers have to report the gun fires before the target is struck? Someone moving past the target at FTL speed could see the target struck, then move past the photon wavefront of the event to a point where the light bouncing off the trigger just as it's getting pulled is arrving. I don't see how this is moving back in time, but merely trading distance for observability. If he tries to FTL travel back to the target to warn him to duck, he'll see events happen as he gets closer to the target and arrive at a bleeding dead body. The activities of the gunfight would appear to speed up as he got closer as he raced back along the photonic wavefronts of events. At no time, though, would he be violating causality anymore than seeing someone die in front of you to a 2 mile distant sniper violates causality just because the sound of the gunshot hasn't gotten to you yet. It's an observational error due to positional change.

There are several inconsistencies in this scenario. We can come at it from a causality-breaking perspective or an equivalency-breaking perspective. The former, relating to the death and trigger-pull events and their respective wavefronts, quite honestly make my head hurt. But since you did ask how causality is threatened, I'll sketch in some thoughts as best I can.

The death event and trigger event each have a wavefront, which we should think of as the edge of a sphere radiating out from that point in time/space. However, each moment before and after those events ALSO has a sphere, like the layers of an onion. Now, what would we see flying FTL in a straight line along the bullet's path, traveling from the victim to the shooter? As we approach the source of the wavefronts (center of the onion), things occur in normal sequence, just as they would were we standing still and experiencing events outer-to-inner. In other words past (outermost layers) to future (innermost). As we pass the center and overtake layers inner-to-outer, we're going to see events in reverse sequence. In this scenario I'm assuming a normal LTL bullet.

1. Unsuspecting victim wanders around.2. Shooter lines up his shot.3. Pulls trigger.4. Bullet comes at victim. Shooter lowers weapon.5. Impact. Shooter waits to see if he scored a hit (impact sphere needs time to reach him.)(Here we are at the center of the victim's timeline sphere.-- Since we are traveling too fast for any of the victim's successive wavefronts to reach us, we're not going to see any of his future. Nor will we ever see shooter's reaction to his shot. By the time he sees it's a hit we'll have passed the center of his onion.)6. Reverse impact. Bullet sucked out of victim's head. Shooter waiting to see what happened.(Center of shooter's timeline sphere.)7. Shooter raises weapon. Bullet travels back towards shooter.8. Bullet enters chamber, sucks explosion back into shell. Trigger pushes shooter's finger out.9. Shooter lines up his shot (in rewind.)10. Resuscitated victim wandering around backwards.

You have to admit that if the FTL inertial frame is not special, i.e. if it's just as valid as the shooter's or victim's, then we have some very broken shit going on. We have causality problems out the wazoo. We are seeing the same events happen twice, once normally and once in reverse. In reverse we're seeing entropy decreasing and all kinds of issues with ballistics, kinetic/potential energy transfers, etc. Hell, if this guy goes far enough he can directly witness (admittedly at a distance) events that happened before he was born (in reverse at first, but just tap the brakes and let the waves come naturally to play in proper order). If watching yourself being born is not time travel, I ask you, what is?

This is getting long, but I did promise an equivalence-breaking approach as well. The simplest way to illustrate it, I think, is this: The FTL ship's cabin is illuminated, is it not?

If yes, then: The traveler is going to measure light within the cabin at its normal speed w/r/t his inertial reference frame (the ship). He's also overtaking light outside the ship, which he's going to measure with negative velocity (how negative depends on how much FTL he's traveling). But some LTL observer outside the ship will measure light within the cabin as FTL. If he sees the cabin lit, and light must travel from the source to the bulkhead, and the light source is FTL, then the light must also be FTL. So now we have two people measuring different speeds for the same light beams; moreover, they are measuring different speeds for different light beams in their own inertial frames. We have a violation of the equivalence principle.

If no, then: The traveler is sitting there in the dark even though his lamp is turned on. Light from the lamp can't reach the forward bulkhead, and the light that hits the aft bulkhead (due to the ship's overtaking it) can't reflect back into the cabin. The ship's cabin is an inertial rest frame in which light is simply broken. Again a violation of the equivalence principle.

why does cartman care if kyle thinks it's t+2sec? he didn't care when he got that luminal message back that said it was t +3days.

++

I mean if they both carried synchronised clocks there would be a major discrepancy between time passed and that doesn't cause any problems.

Ie Cartman would receive the message back at 3.8 years later on his clock but to Kyle's clock it's only 3 days. And when they brought the clock back together the clocks would agree with those times. Time really did pass differently for them due to time dilation... I don't get why there is any causality violations there?

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The scout from C in orbit about A sees A explode. He looks up in the sky and sees C still floating there, as the light arriving is from some time back. Over his ear-mounted Wormhole Radio, though, all he hears is 'AAAAAAAAAAAARRRRGGGGH!!!!!! *boom*'

Also... why does A or C actually explode afterwards? My (probably wrong) inability to get the relativity of simultaenity says that even though C sees C explode and not yet A that's only because the light from the planet A takes x amount of time to get to C. Ie If you were too look at C from A it would be x amount of time behind what it actually is.

So you could then jump in your ship and bo to A to warn it but it's already exploded. It's only the light that hadn't gotten to C first. Otherwise. Doesn't that mean that events which have already happened at C haven't but only when you're at A?

Ie. How can an event which has to take place at the same time (and does from B's perspective) not take place at the same time from A and C's perspective and how can they all be right?

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Okay, so how hard would it be to set up a causality violation with this communication system? The emitter and detector are in different reference frames, so there should be some difference in timing. If we were able to get attosecond resolution on neutrino detectors, would we be able to set up a grandfather paradox?

I'd think it should be possible. We now basically have (SWAG'ing) a physical way to build a closed time like curve. Ie. It'll take a very large number of neutrino emitters/detectors but given enough of them we should be able to break causality... assuming that they are travelling FTL and by our current understanding of C and relativity.

Now, they could be sure of this by setting some point of common reference. Something like, "Look at that rock you're now passing, it looks like your mom's ass!" as the message.

At this point, Kyle could respond ("Shutup, Cartman!"). But, according to him, Cartman is at 0.008 seconds. So, you have to ask, "Which reference frame is 'right'?" They are both in space. They are traveling by each other. Why is one more special than the other?

In the case of using a laser instead, they will both agree on the ordering of messages in their entirety.

why does cartman care if kyle thinks it's t+2sec? he didn't care when he got that luminal message back that said it was t +3days.

++Ie Cartman would receive the message back at 3.8 years later on his clock but to Kyle's clock it's only 3 days. And when they brought the clock back together the clocks would agree with those times. Time really did pass differently for them due to time dilation... I don't get why there is any causality violations there?

Cartman doesn't care how much time Kyle thinks has elapsed. He cares that he gets this information in reply before he asked for it.

Clicky for a very good explanation including enormously helpful diagrams. He's using two sets of travelers because he's making the assumption that an ansible only works between people in the same inertial frame. This does an end-run around the question of whose frame of reference determines what "instantaneous" communication means. The principle is exactly the same with Cartman/Kyle.

why does cartman care if kyle thinks it's t+2sec? he didn't care when he got that luminal message back that said it was t +3days.

++Ie Cartman would receive the message back at 3.8 years later on his clock but to Kyle's clock it's only 3 days. And when they brought the clock back together the clocks would agree with those times. Time really did pass differently for them due to time dilation... I don't get why there is any causality violations there?

Cartman doesn't care how much time Kyle thinks has elapsed. He cares that he gets this information in reply before he asked for it.

Clicky for a very good explanation including enormously helpful diagrams. He's using two sets of travelers because he's making the assumption that an ansible only works between people in the same inertial frame. This does an end-run around the question of whose frame of reference determines what "instantaneous" communication means. The principle is exactly the same with Cartman/Kyle.

Ok cool link though I still don't think that Cartman actually does get information back before he sends it (at least not in this example) in the link you posted you need 4 people to create a causality violation. In addition they need to be moving at velocities high enough to create time dilation effects which create FTL induced CTC's. I'm still not sure how you could do that with only two observers and an ansible?

Having said that, I don't think those diagrams affect the key question for us relativity of simultaenity challenged folk. Ie Personally I get that light conforms to lorentz transformations and Minkowski diagrams. I just don't intuitively (yet) get that reality does. Ie Yeah we get the illusion of causality violations because light takes that amount of time to reach us but the reality is still different.

IE. Do you have any explanations for say two planets being 10 lyrs apart. Each planet sees events happening 10 years after they happen according to the other planet. Now lets take two atomic clocks, synced on one planet and then one is sent to the other. Account for time dilation during travel so you have the clocks still synced. Now have both planets time event A which happens in the solar system of planet A. Planet A's clock says it happens at x time. Planet B's clock says it happens at x + 10yrs time. Now so far as I get the relativity of simultaenity... they're both right? The event took place only once.... but 10 years apart.

If I'm in the same reference frame you are, it doesn't matter how far apart we are. If I'm ten light years away, then when I get information from you, I subtract 10 years and I know when you sent it. Not a problem. We completely agree on what time it is in both places.

In fact, I could imagine setting up a series of beacons in space. A big grid. The clocks are each 1 micrometer from the next. This grid extends for 1000 light years on a side. (It's a lot of very tiny clocks). I can synchronize this grid very easily by starting with one beacon, and moving to the adjacent beacons and setting their clocks. (If 1 micrometer disturbs you, call it epsilon instead).

Now, two people in this grid will always see the same time, and agree. A person that moves, however, does not agree on what time it is. To the grid people, the traveler's clock is slower. To the traveler, the grid clocks are slower. It has nothing to do with the time required to get information from one location to another.

And, just to be clear -- time dilation is a real, measured effect: particle decay being an experiment that has been more than physically verified: we've spent billions building experimental equipment that rely on time dilation for decaying particles.

Having said that, I don't think those diagrams affect the key question for us relativity of simultaenity challenged folk. Ie Personally I get that light conforms to lorentz transformations and Minkowski diagrams. I just don't intuitively (yet) get that reality does. Ie Yeah we get the illusion of causality violations because light takes that amount of time to reach us but the reality is still different.

Several things. Relativity of simultaneity and causality violation are distinct. At or below c, causality is preserved even when observers differ on which of two independent events happened first.

Relativity of simultaneity is not an effect of distance between observers. Observers aren't going to report different ordering of independent events unless they (observers) are in different reference frames, which is to say they're moving w/r/t one another. (The independent events *do* have to be separated spatially, but don't worry about why exactly.)

Light is part of reality. It's not magic. It only seems that way because it's the only thing in everyday experience on earth that moves as fast as it does. If somehow there were massive objects moving around at significant fractions of c, we'd have noticed the non-Newtonian-ness of their motion just as readily. Consider GPS systems. A satellite's clock isn't ticking along the same way one on Earth does such that we have some error in observation that needs to be corrected. The clock up there really is losing time because time really is slower up there. (Don't go too nuts on the GPS thing because special relativity doesn't cover the phenomenon. I'm just using it as an example of everyday, normal, somewhat intuitive conditions where (general as opposed to special) relativistic effects come into play. Read: relativity isn't just for light.)

One reference frame is as good as any other. There's not a correct one and a bunch of wrong ones. Observations in any simply are what really happened. Space and time are experienced differently in different frames, but none is canonical. The Lorentz transform isn't a way to turn an erroneous observation into what "really" happened; it's a way to take one experience of what really happened and see how what really happened was experienced in other frames.

So now let's do relativity of simultaneity. Independent events P and Q occur and are separated in space. It turns out that in frame 1, event P happened first, then event Q. In frame 2, they happened at the same time. In frame 3, event Q happened before event P. Things really did occur this way in each frame. There is no illusion, no observational error, nothing like that. I know it's extremely counter-intuitive, but there is not a canonical order in which P and Q actually happened.

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Planet B's clock says it happens at x + 10yrs time. Now so far as I get the relativity of simultaenity... they're both right? The event took place only once.... but 10 years apart.

No, the event happened once but one party took 10 years to learn of it. Same as if I ate dinner at 7pm, called up my friend at 7:10 and told him I ate ten minutes ago. We both agree that I ate once and only once and it happened at 7pm, because we share a reference frame. If we'd been in different reference frames, we would still agree that I ate once and only once; however, "7pm" isn't going to be a useful descriptor since our clocks run at different rates, and we might disagree about whether I ate before or after some distant event (for example the sun setting at such-and-so coordinates on Neptune). Again, you need observers in relative motion and independent events separated spatially for relativity of simultaneity to apply. If the planets are stationary w/r/t each other, then people on Planet B read their clock, subtract the ten years they know the signal took reaching them, and they'll arrive at the same clock reading Planet A did. For instance say you look at a star 50 ly distant. Provided you and the star are at rest w/r/t each other, you'll agree on when the photon that just hit your eye was emitted -- 50 years ago.

RE Time Dilation: Yep, down with that, i'm familiar with the atomic clock experiments and well... satellites.

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No, the event happened once but one party took 10 years to learn of it. Same as if I ate dinner at 7pm, called up my friend at 7:10 and told him I ate ten minutes ago. We both agree that I ate once and only once and it happened at 7pm, because we share a reference frame. If we'd been in different reference frames, we would still agree that I ate once and only once; however, "7pm" isn't going to be a useful descriptor since our clocks run at different rates, and we might disagree about whether I ate before or after some distant event (for example the sun setting at such-and-so coordinates on Neptune). Again, you need observers in relative motion and independent events separated spatially for relativity of simultaneity to apply. If the planets are stationary w/r/t each other, then people on Planet B read their clock, subtract the ten years they know the signal took reaching them, and they'll arrive at the same clock reading Planet A did. For instance say you look at a star 50 ly distant. Provided you and the star are at rest w/r/t each other, you'll agree on when the photon that just hit your eye was emitted -- 50 years ago.

Still if the event did happen 10 years ago... then why can't I build a wormhole between the two planets? Lets say for simplicities sake that they share the same inertial reference frame (ie they're stationary w/r/t each other). So I build a wormhole which allows instantaneous travel between the two planets. And there should be no causality violations right? And why doesn't this apply to the three planet + bombs thought experiment?

Your reference frame would need to go this >< close up to light speed (for all intents and purposes actually indistinguishable from light speed) to cause the necessary distortion of space-time and shortening of distances to get into any kind of grandfathering paradox.

But here, I do have to pose an interesting though experiment:Can Neutrinos interact at all with such fast reference frames? The only reference frame known to be this fast are photons, and photons cannot interact with neutrinos directly! As far as I am aware (HatMonster please correct me), only mass bearing Hadrones or Leptons can interact with neutrinos. But it is practically impossible to accelerate this kind of matter to light speed. Doing so would convert it into mass-less photons!

So, can there be a paradox if these special neutrinos cannot interact with those reference frames, that would cause a paradox?

Hmm ... interesting though experiments.

LEP accelerated electrons and positrons to 0.9999999999c. The LHC accelerates protons and heavier nuclei like lead to 0.9999999c. Cosmic rays include various nuclei that sometimes are traveling at even higher speeds. So it is not impossible to accelerate matter to very close to light speed; it's just not feasible to do it to more than a few trillion particles at a time.

It is very possible to build an FTL scenario where causality is not violated.

The problem is that with FTL it is possible.

Edit:

I should clarify -- with just those two observers in the same reference frame, you don't have to have a causality violation.

Add another reference frame, and things get weird, quickly.

Ok but lets take the 3 Planet problem. Three planets, A, B and C. B sends missiles to destroy A and C (lets say A and C are 10 light years apart) which should arrive at the same time as B is equidistance from A and C. Wormhole links planets A and C. Now previously it was stated that this would be a causality violation because even though the missiles are sent at the same time and from B's perspective arrive at the same time. From A's perspective you could see the planet blowing up... not see C's planet blow up for 10 years and therefore you've got 10 years to get to C from A (say through the wormhole) and prevent the missile hitting C. Except that..

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No, the event happened once but one party took 10 years to learn of it.

So there's no paradox with the A, B and C planet problem.

You could send a ship from A to C once you see A blow up... but when you get there C has already exploded because it's only the image which took 10 years to get to C. The actual event only took place once.

You know, simple way to test of higher energy neutrinos is the cause. Fire low energy neutrinos from same place at CERN to OPERA. If the results are different, then it's far more likely you've got something. If the results are the same, then it's far likelier you've got an error since low energy neutrinos from supernovae don't travel measurably faster than light, and that has a much larger distance to travel and thus (likely) a much lower margin of error.

You know, simple way to test of higher energy neutrinos is the cause. Fire low energy neutrinos from same place at CERN to OPERA. If the results are different, then it's far more likely you've got something. If the results are the same, then it's far likelier you've got an error since low energy neutrinos from supernovae don't travel measurably faster than light, and that has a much larger distance to travel and thus (likely) a much lower margin of error.

Good idea, it won't rule out low energy neutrinos being able to FTL (if it's not an error in original experiment) but it'll narrow the possibilities.

You know, simple way to test of higher energy neutrinos is the cause. Fire low energy neutrinos from same place at CERN to OPERA. If the results are different, then it's far more likely you've got something. If the results are the same, then it's far likelier you've got an error since low energy neutrinos from supernovae don't travel measurably faster than light, and that has a much larger distance to travel and thus (likely) a much lower margin of error.

In theory, yes, but in practice, it is not so easy.

Lowering the energy of the protons that create the neutrinos leads to a wider angular dispersion in the neutrino beam. Even at the energies being used now, the neutrinos are spread out over several kilometers by the time they reach Italy. Only a small fraction of the neutrinos pass through the detector. Spread it out even more and fewer neutrinos will pass through the detector.

A second issue is that the neutrino scattering cross section becomes smaller at lower energies, so neutrinos passing through the detector are less likely to interact within it.

There are other issues (detector thresholds come to mind), but even with just these two, you can expect a rapid drop in neutrino interactions in OPERA with lower neutrino energies. With fewer events, the error bars on the measurement of c will grow. They would not be able to say if the neutrino speed differs from c by 1 part in 100,000 at even moderately lower neutrino energies because the error bars would be maybe 1 part in 10,000 or worse.

Ahhh, *maybe* it's solved, but maybe not yet. The folks at CERN have said that they did account for time dialation... so we could still see something interesting (even if it is yet another mistake, it can still be an interesting mistake.)

That doesn't make any sense. The GPS satellite clocks have a built-in frequency offset to compensate for time dilation. The whole system wouldn't work at all if they hadn't already accounted for relativity effects.

Not a chance. It's certainly possible, probable even, that something's wrong with OPERA's results, but it isn't nearly as simple as "forgot to correct GPS timing signals for special relativity". First off, GPS signals are already corrected for both SR and GR effect. If they weren't, the whole system would be rife with errors. Taking that preprint's estimate of 30 ns of timing error as correct, that would add roughly 30 feet of error to every GPS position fix anywhere. Secondly, the OPERA timing scheme included checking the sync of their clocks by physically moving a precise timing system from one site to the other and back. They were able to check their clock mismatch directly, and reported it as approximately 2 ns. This was explicitly stated in the OPERA preprint, and is basically a stake through the heart of this "rebuttal".

As I vaguely understand the article, it isn't the adjustment of GPS clocks that's being questioned, it's the difference in reference frames solely due to latitudinal differences in speed between the two sites.

As I vaguely understand the article, it isn't the adjustment of GPS clocks that's being questioned, it's the difference in reference frames solely due to latitudinal differences in speed between the two sites.

The I don't know enough to feel entirely confident rebuttal to the latitude difference - is - it can't be; or the reference clocks would not match after the physical transfer. 2ns is reported about; that puts and upper limit on the difference, and it's not big enough.

As I vaguely understand the article, it isn't the adjustment of GPS clocks that's being questioned, it's the difference in reference frames solely due to latitudinal differences in speed between the two sites.

No, that's never mentioned in the rebuttal preprint (PDF link). If you look at pg 3 of the preprint, the calculation is based strictly on the orbital velocity of the GPS satellites, and doesn't make any reference to the latitudes of the two ground stations. And note on page 2, the author uses an effective velocity of "c + v" for a photon in a particular frame, which is just a big fat FAIL.

And note on page 2, the author uses an effective velocity of "c + v" for a photon in a particular frame, which is just a big fat FAIL.

wow, i missed that. was this written by a high schooler?

if you don't understand relativity enough to get why that's wrong, that's ok. most people don't. if you don't understand relativity enough to get why that's wrong but continue then to base a rebuttal of a scientifically sound paper* on it then you're an idiot.

* the paper's science is sound, as far as anyone can tell; it is the result that is in question.

And note on page 2, the author uses an effective velocity of "c + v" for a photon in a particular frame, which is just a big fat FAIL.

wow, i missed that. was this written by a high schooler?

if you don't understand relativity enough to get why that's wrong, that's ok. most people don't. if you don't understand relativity enough to get why that's wrong but continue then to base a rebuttal of a scientifically sound paper* on it then you're an idiot.

* the paper's science is sound, as far as anyone can tell; it is the result that is in question.

--RC

As I was hinting at in my previous post, there is not necessarily an inconsistency. In the satellite's frame, there is a photon moving to the right at c, and the detector (the earth) is moving to the left at v. After a time tau, the photon and detector meet, in which time the total distance traversed (by both... which is equal to the original separation at the time of photon emission) is.... (c+v)*tau.

Jacotus has it exactly right. Read the paper. They aren't adding the velocity of a frame to the velocity of a photon - that would be bullshit. They're adding the distance traveled by the detector to the distance traveled by the photon. If you then factor out time you get a factor that looks like c + v, but doesn't involve anything superluminal.

The paper is simplistic, but there's nothing that obvious wrong with it.

Exactly. Basically, we can't draw any solid conclusions about FTL travel violating causaility, because have no math that has been tested to be relevant in FTL situations - Lorentz transformations all go to infinity when you put in C, or else to zero. They're asymptotic when they approach C, and we have not been able to prove that the are symmetrically applicable to particles travelling at FTL speeds - so we have no way of knowing that the projections we throw out using those equations are in fact relevant.

If the math shows a huge divergence when you approach a limit, it's quite likely that- IF - there exists FTL travel, it will require new math that is both applicable to FTL AND which reduces to explain all phenomena that goes at LTL speeds - sort of like how general relativity encompasses classical motion - only on a higher level.

You and troy said you had trouble visualizing causality and relativity of simultaneity. I was responding to your hypothetical FTL bullet scenario. If any observer sees the target struck before the gun is fired, causality is out the window.

Throwing out of the window your notion of causality is no bigger deal than throwing out notion that different observers agree on ordering of events happening in the different points of space. If I press a button that makes something happen 10 seconds ago (according to you) at Alpha Centauri, that's a causal relationship just fine - there's cause, there's effect 10 LY and -10 seconds away, it's just that observers no longer agree that cause has smaller t coordinate than effect.If I press a button here and make something happen 10 seconds ago here, then you got a big problem.

The reason we care about causality is the grandfather paradoxes, for which not only you need to go into the past, you need to go into the past at the starting point, and that requires your FTL channels to be very close and moving very fast relatively to each other etc, very extreme conditions which could well be impossible according to whatever laws govern the FTL channels.

re: the equivalence principles, for gravity vs acceleration (GR), what we actually observe is that effects of gravity and acceleration on the point masses are indistinguishable to a very high degree of accuracy, i.e. we have somewhat good enough reason to think that those are the same thing and GR is correct. And we haven't found any other effects of gravitational field, but we don't know there isn't any, and GR does not say there can not be any. We do not know that the effects of masses on all things are indistinguishable from acceleration.

Ditto for the equivalence of different reference frames, we have observed that transformations work out this way, and that's it, we don't know that the different reference frames are truly equivalent (actually there's the cosmic background radiation that sets a preferred frame at every point).

There is even an everyday example of how the equivalence may not exist due to prevalent background: rotational velocity. If the entire universe was rotating, due to the frame dragging effect, you wouldn't be able to sense such rotation! The preferred rotating frame of reference, one with zero angular velocity relatively to stellar background, that's in a way the gravitational effect of those far away stars. The inertial frame in centre of the Earth is (very slowly) spinning relatively to far away stars.

Basically, a similar experiment in the same place looked at the energy spectrum of their neutrinos from CERN. The spectrum suggests that the neutrinos did not travel faster than the speed of light.

Quote:

What is important is that there is a clean and simple relationship between the superluminal speed and the rate of decrease of the neutrino energy.

Right, the observed shift of perigee of mercury ruled out using Newtonian physics and it not conforming with any possible extra planet's influence. Hahaha.

Sigh. It would be funny if it wasn't so sad. The original measurement may well have been an error, but you don't rule out a speed measurement based on your 'guess' how to calculate the spectra at FTL where a bunch of relevant formulas frigging go imaginary, square root of negative numbers style. This is just very stupid reporting here. At most, the study has shown that a: some formulas must be inapplicable at FTL [hardly a big surprise] or b: it was not the neutrino that was moving at FTL. [we don't really know what was moving at FTL and how, for all we know it could as well have hopped through space]

Einstein was wrong about the "Time" half of general relativity and all that "space/time".

Of course, the difficulty is separating "time" from "space" in measurements to begin with. So it made a very good amount of sense to try and treat both as fundamentally linked. But just because they are linked by problems of observation doesn't necessarily mean they are so fundamentally linked in reality.

Throw out relativity's time implications and you get rid of closed timelike curves, tachyons, and all that other potential headache inducing stuff. Instead assume C and all other effects are due to effects of space and space itself. You can be the one to work it out and get the nobel prize.

Time may be some sort of homogeneous frame of reference, just the frame of reference for everything. FTL Neutrinos are then a problem of space and how things move through it. A problem not totally satisfied by General Relativity anyway, visa vis it doesn't seem to fit with things like the plank length despite decades of trying.

If there is a rocket that is exactly 1 light year long, with person A at the tip of the rocket, and person B at the very end of the rocket. The rocket itself is traveling at the speed of light. Person A is told to point a flash light at Person B, and to turn the flash light on and off in exactly 1 minute intervals.

The question: At what speed of intervals does Person B see the flashes of light from Person A?